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Correlation Decay and Tractability of CSPs Brown-Cohen, Jonah Raghavendra, Prasad Constraint Satisfaction Polymorphisms Linear Equations Correlation Decay The algebraic dichotomy conjecture of Bulatov, Krokhin and Jeavons yields an elegant characterization of the complexity of constraint satisfaction problems. Roughly speaking, the characterization asserts that a CSP L is tractable if and only if there exist certain non-trivial operations known as polymorphisms to combine solutions to L to create new ones. In this work, we study the dynamical system associated with repeated applications of a polymorphism to a distribution over assignments. Specifically, we exhibit a correlation decay phenomenon that makes two variables or groups of variables that are not perfectly correlated become independent after repeated applications of a polymorphism. We show that this correlation decay phenomenon can be utilized in designing algorithms for CSPs by exhibiting two applications: 1. A simple randomized algorithm to solve linear equations over a prime field, whose analysis crucially relies on correlation decay. 2. A sufficient condition for the simple linear programming relaxation for a 2-CSP to be sound (have no integrality gap) on a given instance. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Jonah Brown-Cohen and Prasad Raghavendra 2016 Is Part Of LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2016.79 urn:nbn:de:0030-drops-62064 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.79 eng https://creativecommons.org/licenses/by/3.0/legalcode